Publication detail

# Conditional Stability of Weakly Delayed Planar Linear Discrete Systems

DIBLÍK, J. HALFAROVÁ, H. ŠAFAŘÍK, J.

Original Title

Conditional Stability of Weakly Delayed Planar Linear Discrete Systems

English Title

Conditional Stability of Weakly Delayed Planar Linear Discrete Systems

Type

conference paper

Language

en

Original Abstract

The paper deals with discrete planar systems x(k + 1) = Ax(k) + \sum_{l=1}^{n}B^{l}x(k − m_{l}), k \geq 0 where m_{1}, m_{2}, . . . ,m_{n} are constant integer delays, 0 < m_{1} < m_{2} <...< m_{n}, A,B_{1}, ...,B_{n} are constant 2 × 2 matrices, A = (a_{ij}), B_{l} = (b_{ij}^{l}), i, j = 1, 2, l = 1, 2, . . . , n and x: {−m_{n},−m_{n} + 1, . . . } \rightarrow R^{2}. New results related with what is called conditional stability and asymptotic conditional stability are derived.

English abstract

The paper deals with discrete planar systems x(k + 1) = Ax(k) + \sum_{l=1}^{n}B^{l}x(k − m_{l}), k \geq 0 where m_{1}, m_{2}, . . . ,m_{n} are constant integer delays, 0 < m_{1} < m_{2} <...< m_{n}, A,B_{1}, ...,B_{n} are constant 2 × 2 matrices, A = (a_{ij}), B_{l} = (b_{ij}^{l}), i, j = 1, 2, l = 1, 2, . . . , n and x: {−m_{n},−m_{n} + 1, . . . } \rightarrow R^{2}. New results related with what is called conditional stability and asymptotic conditional stability are derived.

Keywords

Conditional stability, conditional asymptotic stability, weakly delayed system, discrete system

RIV year

2015

Released

25.04.2015

Publisher

WSEAS Press

Location

Kuala Lumpur, Malaysia

ISBN

978-1-61804-302-3

Book

Recent Advances in Mathematical and Computational Methods

Edition

Mathematics and Computers in Science in Science and Engineering Series | 44

Pages from

111

Pages to

117

Pages count

7

URL

Documents

BibTex

```
@inproceedings{BUT123370,
author="Josef {Diblík} and Hana {Halfarová} and Jan {Šafařík}",
title="Conditional Stability of Weakly Delayed Planar Linear Discrete Systems",
annote="The paper deals with discrete planar systems
x(k + 1) = Ax(k) + \sum_{l=1}^{n}B^{l}x(k − m_{l}), k \geq 0
where m_{1}, m_{2}, . . . ,m_{n} are constant integer delays, 0 < m_{1} < m_{2} <...< m_{n}, A,B_{1}, ...,B_{n} are constant 2 × 2 matrices, A = (a_{ij}), B_{l} = (b_{ij}^{l}), i, j = 1, 2, l = 1, 2, . . . , n and x: {−m_{n},−m_{n} + 1, . . . } \rightarrow R^{2}. New results related with what is called conditional stability and asymptotic conditional stability are derived.",
address="WSEAS Press",
booktitle="Recent Advances in Mathematical and Computational Methods",
chapter="123370",
edition="Mathematics and Computers in Science in Science and Engineering Series | 44",
howpublished="print",
institution="WSEAS Press",
year="2015",
month="april",
pages="111--117",
publisher="WSEAS Press",
type="conference paper"
}
```